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ESTIMATION OF THE FRACTIONAL DIFFERENCE PARAMETER IN THE ARIMA( p, d, q ) MODEL USING THE SMOOTHED PERIODOGRAM
Author(s) -
Reisen Valderio A.
Publication year - 1994
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1994.tb00198.x
Subject(s) - mathematics , estimator , autoregressive integrated moving average , autoregressive model , long memory , hurst exponent , series (stratigraphy) , autoregressive fractionally integrated moving average , statistics , range (aeronautics) , time series , econometrics , volatility (finance) , paleontology , materials science , composite material , biology
. In recent work on time series analysis considerable interest has been focused on series having the property of long memory. Long memory is a characteristic of time series in which the dependence between distant observations is not negligible. The model that has been most frequently studied, which in some situations shows properties of long memory, is based on the autoregressive integrated moving‐average ARIMA( p, d, q ) process. Hosking (Fractional differencing, Biometrika 68 (1) (1981), 165–76) generalized this model by permitting the degree of differencing d to take fractional values. He then demonstrated that for d in the range 0 < d < 0.5 the process is stationary and possesses the long memory property. Our study is based on the ARIMA( p, d, q ) model when d takes any real non‐integer value in the interval (‐0.5, 0.5). The main aim of our study is to examine methods for estimating the parameters of this model. For estimating d we suggest an estimator based on the smoothed periodogram. Using an empirical approach we compare this estimator with other which are well known in the literature of long memory models, e.g. the raw periodogram regression method and the Hurst coefficient method.